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Rigid geometry and its application to number theory

Research Project

Project/Area Number 17340002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

FUJIWAWA Kazuhiro  Nagoya University, 大学院・多元数理科学研究科, 教授 (00229064)

Co-Investigator(Kenkyū-buntansha) UZAWA Tohru  名古屋大学, 大学院・多元数理科学研究科, 教授 (40232813)
KONDO Shigeyuki  名古屋大学, 大学院・多元数理科学研究科, 教授 (50186847)
FUJINO Osamu  名古屋大学, 大学院・多元数理科学研究科, 准教授 (60324711)
加藤 文元  京都大学, 大学院・理学研究科, 准教授 (50294880)
斎藤 秀司 (斉藤 秀司)  東京大学, 大学院・数理科学研究科, 教授 (50153804)
斉藤 毅  東京大学, 大学院・数理科学研究科, 教授 (70201506)
Co-Investigator(Renkei-kenkyūsha) KATO Fumiharu  京都大学, 大学院・理学研究科, 准教授 (50294880)
SAITO Shuji  東京大学, 大学院・数理科学研究科, 教授 (50153804)
SAITO Takeshi  東京大学, 大学院・数理科学研究科, 教授 (70201506)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥16,200,000 (Direct Cost: ¥14,100,000、Indirect Cost: ¥2,100,000)
Fiscal Year 2008: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2007: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2006: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2005: ¥3,900,000 (Direct Cost: ¥3,900,000)
Keywordsリジッド幾何学 / 形式幾何学 / 志村多様体 / Zariski-Riemann 空間 / 双有理幾何学 / 非可換類体論 / Zariski-Riemann空間
Research Abstract

研究分担者, 連携研究者の協力の下, リジッド幾何学の基礎付けを研究した. 特に, EGA III より一般の枠組みで形式幾何学を展開している. 基礎付けの応用としてスキームおよび代数空間の永田コンパクト化の構成など, 代数幾何学での基本的な定理がある. また, 可換環の完備化の理論の(非ネーター環を含む)再構成等でも新たな見方を提示しており, 形式スキームとしてのネーター性がなくてもリジッド空間としてのネーター性があれば 十分であることを発見した. これは特にR. Huber によるadic space の理論が成立する枠組みを明快にするものである.基礎付け一般の結果は加藤文元(京都)との共著として発刊する予定である.

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (31 results)

All 2009 2008 2007 2006 Other

All Journal Article (17 results) (of which Peer Reviewed: 11 results) Presentation (14 results)

  • [Journal Article] Ramification theory for varieties over a perfect field2008

    • Author(s)
      Kato, K, Saito, T.
    • Journal Title

      Ann. Of Math. 168

      Pages: 33-96

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maximal components of Noether-Lefschetz locus for Beilinson-Hodge cycles2008

    • Author(s)
      Saito, S, Asakura, M
    • Journal Title

      Math. Ann. 341

      Pages: 169-199

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Shimura variety having Mumford's fake projective plane as a connected component2008

    • Author(s)
      Kato, F.
    • Journal Title

      Math. Z 259

      Pages: 631-641

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Shimura variety having Mumford's fake projective plane as a connected component2008

    • Author(s)
      Kato, F.
    • Journal Title

      Math. Z. 259

      Pages: 631-641

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eamification theory for varieties over a perfect field2008

    • Author(s)
      Kato, K., Saito, T.
    • Journal Title

      Ann. of Math. 168

      Pages: 33-96

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximal components of Noether-Lefschetz locus for Beilinson-Hodge cycles2008

    • Author(s)
      Saito, S., Asakura, M.
    • Journal Title

      Math. Ann. 341

      Pages: 169-199

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic cycles and Mumford-Griffiths invariants, Amer, J2007

    • Author(s)
      Lewis, James D, Saito, S.
    • Journal Title

      Amer, J. of Math. 129

      Pages: 1449-1499

    • Related Report
      2008 Final Research Report
  • [Journal Article] The characteristic class and ramification of an l-adic etale sheaf2007

    • Author(s)
      Abbes, A, Saito, T.
    • Journal Title

      Invent. Math. 168

      Pages: 567-612

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rigid analytic geometry2007

    • Author(s)
      Kato, F.
    • Journal Title

      Sugaku expositions 20

      Pages: 65-95

    • NAID

      10013701820

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The characterisitic class and ramification of an l-adic etale sheaf2007

    • Author(s)
      Abbes, A., Saito, T.
    • Journal Title

      Invent. Math. 168

      Pages: 567-612

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Moduli of K3 surfaces and complex ball quotients2007

    • Author(s)
      Dolgachev, L., Kondo, S.
    • Journal Title

      Progr. Math. 260

      Pages: 43-100

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Maximal subgroups of the Mathieu group M_ <23> and symplectic automorphisms of supersingular K3 surfaces2006

    • Author(s)
      Kondo, S.
    • Journal Title

      Int. Math. Res. Not. Art. ID 71517

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rigid geometry and applications2006

    • Author(s)
      Fujiwara, K, Kato, F.
    • Journal Title

      Advanced Studies in Pure Math 45

      Pages: 327-386

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Galois deformations and arithmetic geometry of Shimura varieties,2006

    • Author(s)
      Fujiwara, K
    • Journal Title

      Proceedings of the International Congress of Mathematicians Madrid 2006

      Pages: 347-371

    • Related Report
      2008 Final Research Report
  • [Journal Article] Galois deformations and arithmetic geometry of Shimura varieties2006

    • Author(s)
      Fujiwara, K
    • Journal Title

      Proceedings of the International Congress of Mathematicians Madrid 2006 2

      Pages: 347-371

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Rigid geometry and applications2006

    • Author(s)
      Fujiwara, K., Kato, F.
    • Journal Title

      Advanced Studies in Pure Math. 45

      Pages: 327-386

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Rigid geometry and its applications

    • Author(s)
      Fujiwara, K., Kato, F.
    • Journal Title

      Advanced Studies in Pure Mathematics (to appear)

    • Related Report
      2005 Annual Research Report
  • [Presentation] Compactifications of schemes and algebraic spaces2009

    • Author(s)
      Fujiwara, K.
    • Organizer
      Arithmetic Algebraic Geometry Related to Moduli Spaces
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2009-01-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Compactifications of schemes and algebraic spaces2009

    • Author(s)
      Fujiwara, K.
    • Organizer
      Arithmetic Algebraic Geometry Related to Moduli Spaces
    • Place of Presentation
      東京大学
    • Year and Date
      2009-01-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Non-symplectic automorphisms of K3 surfaces and ball quotients2008

    • Author(s)
      Kondo, S.
    • Organizer
      Conference on Moduli spaces
    • Place of Presentation
      Warwick, UK
    • Year and Date
      2008-07-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Topological rings in rigid geometry2008

    • Author(s)
      Kato, F.
    • Organizer
      Motivic Integration and its Interaction with Model Theory and Non-Archimedean Geometry
    • Place of Presentation
      ICMS, Edinburgh
    • Year and Date
      2008-05-15
    • Related Report
      2008 Final Research Report
  • [Presentation] A conjecture of Colliot-Th'el ene on zero-cycles over local fields2007

    • Author(s)
      Saito, S.
    • Organizer
      G'eom'etrie arithm'etique et vari'et'es rationnelles
    • Place of Presentation
      CIRM, Luminy
    • Year and Date
      2007-12-07
    • Related Report
      2008 Final Research Report
  • [Presentation] The moduli of plane quartics and Borcherds products, Modular forms and moduli spaces2007

    • Author(s)
      Kondo, S.
    • Organizer
      Satellite meeting for Festival dedicated to 300th birthday of Leonhard Euler
    • Place of Presentation
      Saint-Petersburg, Russia
    • Year and Date
      2007-07-04
    • Related Report
      2008 Final Research Report
  • [Presentation] Wild ramification and the characteristic cycle of an 1-adic sheaf2007

    • Author(s)
      Saito, T.
    • Organizer
      Conference Dedicated to the Mathematical Heritage of Spencer J. Bloch
    • Place of Presentation
      Fields Institute, Toronto
    • Year and Date
      2007-03-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Iwasawa theory and non-abelian class field theory2007

    • Author(s)
      Fujiwara, K.
    • Organizer
      MFO
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2008 Final Research Report
  • [Presentation] Iwasawa theory and non-abelian class field theory2007

    • Author(s)
      Fujiwara, K.
    • Organizer
      CIRM
    • Place of Presentation
      Luminy, France
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Ramification of schemes over a local field (joint work with K. Kato)2006

    • Author(s)
      Saito, T.
    • Organizer
      Arithmetic Algebraic Geometry,
    • Place of Presentation
      El Escorial, Spain
    • Year and Date
      2006-09-04
    • Related Report
      2008 Final Research Report
  • [Presentation] Weak Bloch-Beilinson conjecture for zero-cycles over local fields2006

    • Author(s)
      Saito, S.
    • Organizer
      Cohomological approaches to rational points
    • Place of Presentation
      MSRI, Berkeley
    • Year and Date
      2006-03-29
    • Related Report
      2008 Final Research Report
  • [Presentation] The moduli of 8 points on the projective line and automorphic forms2006

    • Author(s)
      Kondo, S.
    • Organizer
      Modular forms, Schiermonnikoog
    • Place of Presentation
      Netherlands
    • Related Report
      2008 Final Research Report
  • [Presentation] Problems around Hecke algebras for GL(2)2006

    • Author(s)
      Fujiwara, K.
    • Organizer
      Arithmetic Algebraic Geometry
    • Place of Presentation
      Kyoto University(Kyoto, Japan)
    • Related Report
      2008 Final Research Report
  • [Presentation] Galois deformations and arithmetic geometry of Shimura varieties2006

    • Author(s)
      Fujiwara, K.
    • Organizer
      Internation Congress of Mathematicians
    • Place of Presentation
      Madrid, Spain
    • Related Report
      2008 Final Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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